Chow C.
asked • 03/01/20Show that
(1+tan pi/6 . tan pi/3) + (tan pi/6 - tan pi/3) = sec2pi/6. sec2pi/3
Mark M. answered • 03/01/20
Mathematics Teacher - NCLB Highly Qualified
sec2 π/6 = 1 + tan2 π/6
sec2 π/3 = 1 + tan2 π/3
(sec2 π/6)(sec2 π/3)
(1 + tan2 π/6)(1 + tan2 π/3)
1 + tan2 π/6 + tan2 π/3 + (tan2 π/6)(tan2 π/3)
QED
Sam Z. answered • 03/01/20
Math/Science Tutor
Just want make sure; on the first formula; is that a decimal?
Chow C.
Hello Sam. That decimal point or full stop that i have used between (1+tan pi/6 . tan pi/3) and others is for into/multiplication. I also have the photo of the question written but I'm not sure how can we post the photo here. Thanks for taking the time to look into this question. I need help in this question.03/01/20
Sam Z.
You're saying the . is a mult sign? if so use *. As for "pi" it looks like you're dealing with rad; so pi=180. You get (1+tan30)(tan60)+(tan30-tan60)=(1/cos30)^2. -5.405*.32 + -6.405-.32 = 6.482^2 -1.73 + -6.73 = 42.016.......... -8.455........... ?????????????03/01/20
Chow C.
Yes. Thanks for the idea there! So the question looks like this then (1+tan pi/6 * tan pi/3) + (tan pi/6 - tan pi/3) = sec^2pi/6*sec^2pi/3 So here we just need to show that LHS = RHS. Also sec^2pi/6*sec^2pi/3 was simplified to (1/cos30)^2 Can you explain me please there? I have checked the question a lot of times I haven't been able to prove that at all. By the Answer above it seems that both are not equal or can not be simplified to show LHS = RHS?03/01/20
Chow C.
Here's also the photo of Problem in my book. https://ibb.co/84L9PG303/01/20
Sam Z.
This time I'll stick with USA. Pi=3.1415962...... (1+tan3.14/6)(tan3.14/3)+(tan3.14/6-tan3.14/3)=(1/cos3.14/6)^2. (1+tan.5236)(tan1.047)+(.0091-.0182)=(1/.998)^2 1.009 * .0182 + (-.00914) = 1 .0184 + (-.00914)=.02758 =1???03/02/20
Sam Z.
I'm trying 1 more time: This time "pi" will stay as is; though the rest is in radians. (1+tan3.14/6)(tan3.14/3)+(tan3.14/6-tan3.14/3)=(1/cos3.14/6)^2 1.577 * 1.732 + ( .577-1.732) =1.154^2 2.732 + (-1.1547) =1.333 1.5773 That's better.03/02/20
Chow C.
I really appreciate the effort and thanks for bringing it so close. Now i actually use that solution too for showing that they are approximately equal. Thanks Again.03/03/20
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Chow C.
Hello Mark. First of all thanks for taking the time and effort to help me out! Can you help me with the last part where in the multiplication of (1 + tan2 π/6)(1 + tan2 π/3) The answer is 1 + tan2 π/6 + tan2 π/3 + (tan2 π/6)(tan2 π/3) In the question it was to show that (1+tan pi/6 . tan pi/3) + (tan pi/6 - tan pi/3) So we mostly got it but in the end can we show tan2 π/6)(tan2 π/3) As (tan pi/6 - tan pi/3) So that would bring it to exactly equal. I was not able to understand that part! I kindly request you to please explain me there :) Thanks Again. I appreciate the huge efforts!03/03/20